For polyatomic molecules, extracting vibrational frequency shifts from spectra recorded under shock loading conditions is complicated by anharmonic coupling of modes and thermal population of low lying vibrational levels, which produce hot bands in the vibrational spectra. Most vibrational frequency shifts with shock pressure reported in the literature have been extracted from inadequately resolved spectral bands fitted with single Gaussians. This paper shows that, in general, for polyatomic molecules, the effect of the hot bands is to push the centroid of the fitted Gaussian away from the frequency of the vibrational fundamental. The direction and magnitude of this effect requires knowledge of the anharmonic coupling coefficients (which are in all likelihood also pressure dependent). To completely characterize the intra- and intermolecular potentials, it is therefore necessary to use the highest spectral resolution possible, and to independently measure or calculate the pressure and temperature dependence of the anharmonic coupling coefficients for the molecules of interest.